The Influence of Correlated Variance Structure in Relative Isotopic Abundances on Nondestructive Assay Results?

: Two important and commonly applied approaches to the nondestructive assay of special nuclear materials for materials accountancy and nuclear safeguards are CAL-ISO and NCC-ISO. In CAL-ISO the heat flow from an item is measured using calorimetry, and the mass of nuclear material present is inferred from the effective power parameter using the estimated relative isotopic composition obtained from gamma spectroscopy. On the other hand, in NCC-ISO the spontaneous fission rate is obtained by measuring the item in a neutron coincidence counter, and the mass of nuclear material present is inferred using the effective 240Pu weight fraction inferred from the relative isotopic composition obtained from gamma spectroscopy. In both cases, the parameters needed to interpret the measurement, effective power and Pu-240-effective, respectively, are linear combinations of the isotopic composition (weight fraction of each contributory nuclide), and in both cases, for field measurements the estimated isotopic composition usually comes from a high-resolution gamma spectrum analysis. The estimated relative isotopic composition is expected to exhibit nonzero covariance if for no other reason than it is a normalized vector. The gamma spectrum analysis is quite involved and introduces other dependences which are not easy to assess (although we are working on this). However, in practice we have never seen a reported covariance or correlation matrix for relative weight fraction estimation– no matter how it was obtained, including mass spectrometry used in the production of certified reference materials. Anticipating that such information will become routinely available in the future, being no more than a matter of good metrology practice, we show how to propagate the variance structure into the total measurement uncertainty of the material mass. By numerical example, we illustrate the derived algebraic expressions. The approach described, or something equivalent such as simulation, can be readily adopted into future measurement protocols and represent best practices.